English words do not inflect much; in fact you could claim that English is almost a non-inflectious language.

The only real inflection allowed of English adjectives is that of positive, comparative and superlative:
odd, odder, oddest
and a few notoriously irregular forms like
good, better, best.

We have two ways of forming the far more common regular forms: by affixation
odd, odder, oddest
or by periphrasis, such as
complex, more complex, most complex.

Although many adjectives can follow either method, and there are some preferences (which may be determined by dialect and/or register), there is a general rule which works quite well. In most cases, adjectives with just one syllable can inflect by affixation, as with odd above, unless they are the participle of a verb. Many polysyllabic adjectives and all participles normally prefer the periphrastic route, like complex above.

As far as English goes, that is a pretty simple rule of thumb, and works almost all the time. Take prosody into account, and you will find it quite reliable, except with one group of monosyllabic adjectives:
right, wrong, fake, ill, real, cross, like, loath, prime, worth
(I reinforce that I am referring here only to the adjectival sense of those words, some of which are also used for other purposes).

Although some of these do occasionally crop up using affixation, they are very unusual, and to most English speakers words like
*rightest, *wronger, *illest, *realer
could not be *wronger.

So why just these ten words? Is this list totally arbitrary?

Is seems to be. You could suggest that some should not really form comparatives or superlatives at all; you could not be more wrong, though. You could suggest that those forms are prosodically defective (sound ‘orrible), but if that were the case the list would be much longer, not lighter. You could even suggest that affixed forms became ‘frozen out’ from their origin, as most came from Old English, except that prime comes from the Latin primus, and real from realis.

So it does appear to be a totally arbitrary list. How we learn it, and don’t speak *wronger to make others *crosser, is another one of the mysteries of language.

References

This list is given in Huddleston and Pullum’s Cambridge Grammar of the English Language, p. 1583, where the periphrastic form is described as being analytical, and formation by affixation as being inflectional.
However my treatment above is based on the slightly different account in Bauer, Lieber and Plag (2013) The Oxford Reference Guide to English Morphology, p. 111.